在兴奋-抑制混沌神经元网络中有序波的自发形成

大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%, 21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

General solution of a system of equations for acoustic wave propagation in a partially ionized gas in an external electric field

In this paper a system of equations describing the propagation of acoustic waves in multicomponent partially ionized plasma in an external electric field is solved generally, when these waves are generated by an external neutral sound wave in plasma. The equations are solved by means of Laplace transformation. It has been found that a sound wave generates a group of waves with different frequencies and wave vectors. For the sake of comparison, the solution without an external field and the linear solution in the form of waves having the same frequencies as the frequency of the excitation wave are given.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

From bell-shaped solitary wave to W/M-shaped solitary wave solutions in an integrable nonlinear wave equation

The bifurcation theory of dynamical systems is applied to an integrable nonlinear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.     

Resonant excitation and nonlinear evolution of waves in the equatorial waveguide in the presence of the mean current

We study interactions of planetary waves propagating across the equator with trapped Rossby or Yanai modes, and the mean flow. The equatorial waveguide with a mean current acts as a resonator and responds to planetary waves with certain wave numbers by making the trapped modes grow. Thus excited waves reach amplitudes greatly exceeding the amplitude of the incoming wave. Nonlinear saturation of the excited waves is described by an amplitude equation with one or two attracting equilibrium solutions. In the latter case spatial modulation leads to formation of characteristic defects in the wave field. The evolution of the envelopes of long trapped Rossby waves is governed by the driven complex Ginzburg-Landau equation, and by the damped-driven nonlinear Schr?dinger equation for short waves. The envelopes of the Yanai waves obey a simple wave equation with cubic nonlinearity.     

Modelling of Internal and Surface Waves of the Real Ocean in the Large Thermostratified Experimental Tank at the Institute of Applied Physics of the Russian Academy of Sciences

We discuss the results of studies of surface-wave transformation by nonuniform flows, performed in the tank of the Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), and the results of modelling of the influence of iceberg motion on regular background internal waves in the subsurface pycnocline.Transformation of surface waves in the flow field past an immersed sphere is studied both experimentally and theoretically. It is shown that even fairly weak nonuniform flows can cause noticeable changes in the surface-wave field. The sizes of the spatial region in which the characteristics of the surface waves are changed exceed considerably the sizes of the nonuniform-flow region. It is found that the nonlinearity of surface waves leads to an increase in the variability of the surface-wave amplitude in a broad frequency range. The proposed theoretical model describes well the main experimentally observed features of the transformation of nonlinear surface waves in the nonuniform-flow field.It is proved experimentally that background internal waves with frequencies close to those of internal waves in an iceberg wake lead to a considerable transformation of the field of lee waves. The parameters of the resulting wave system are independent of characteristic horizontal sizes of the iceberg model and the length of the internal wave. The total wave system is stationary in the entire velocity range of the model in the case of counterpropagation of background waves. In the case of copropagation of background waves, the nature of the wave system depends on the ratio between the towing velocity and the phase velocity of background waves. In particular, the wave system in the wake can have both a pronounced nonstationary nature and a typical stationary phase pattern.     

Laboratory and modeling study on modulated wave properties

Development of Benjamin?Feir instability is investigated under laboratory conditions and by analytical modeling. Nonlinear properties of the wave train with discrete spectrum are also investigated. The mechanically generated waves are composed of several discrete waves, while the newly generated harmonics are still combined into discrete spectra with the same frequency step. The technique proposed in this study allows us to study accurately the nonlinear variations in main properties of each harmonic with fixed frequency, such as amplitude, phase speed, and wavenumber along the wave tank together with velocities of wave packet crests, especially for the large transient waves. The phase speeds of short waves increase near large transient waves, and the velocities of longer waves are close to the values determined by the linear theory of waves. The relative long wave accompanied by short waves can dramatically change the local kurtosis and skewness of the wave field. They may play an important role for the generation of large transient wave and provide an opportunity for triggering of the freak waves.     

Dispersion characteristics of surface magnetostatic waves with dissipation

It is shown that unlike undamped waves, the dispersion characteristics of spin surface waves with dissipation have a maximum wave number at which there is a downward reversal in the dispersion curve of a wave number. This forms the upper branch of a dispersion curve with inverse dispersion and high attenuation, leading to an unclear frequency dependence of the wave vector. The lower primary dispersion branch corresponds to waves with forward dispersion, and attenuation is proportional to the small parameter of dissipation. However, the coefficient of wave attenuation grows sharply near the maximum wave number. Some angular and frequency limits of surface wave propagation change as well.     

Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water

When the face of a finite solid elastic cylinder is ensonified by an acoustic wave, a variety of backscattering contributions associated with acoustic wave coupling into elastic waves are observed. A significant backscattering enhancement is observed for tilts such that the acoustic wave is incident on the face of the cylinder in the vicinity of the coupling angle for launching Rayleigh waves across the face. The observed backscattering indicates that the Rayleigh waves are reflected at the edge of the face and subsequently radiate acoustic waves in the backscattering direction. The measured backscattering is compared to an approximate theoretical prediction. Approximating the focusing of the Rayleigh wave after reflection at the (circular) edge by a Gaussian beam pressure distribution on the cylinder's face yields simple expressions for the amplitude which are consistent with the measurements. In the vicinity of end-on incidence, other backscattering contributions due to the reflection of waves traveling down the length of the cylinder are observed. There is also evidence of a face-traversing longitudinal wave for slightly tilted cylinders.     

Generation of Sound by a Two-Dimensional Gas of Indirect Dipolar Excitons

The generation of acoustic waves by a gas of two-dimensional indirect dipolar excitons irradiated by an electromagnetic wave has been studied by the deformation potential method. It has been shown that an acoustic wave propagating into the interior of the isotropic substrate is generally a superposition of longitudinal and transverse waves. At high frequencies of electromagnetic perturbation, the generated acoustic wave degenerates almost completely into a transverse wave. The amplitudes of both waves have been calculated. Their frequency dependences at temperatures above and below the temperature of condensation of the exciton gas have been determined.     

Damping rates of waves in a switched magnetoplasma medium:longitudinal propagation

The interaction of a circularly polarized electromagnetic wave with a switched-on magnetoplasma medium is considered. A static magnetic field in the direction of propagation is assumed to be present, resulting in longitudinal propagation. The incident wave splits into three waves whose frequencies are different from that of the incident wave. It is shown that these waves ultimately damp out if the plasma is even slightly lossy. The damping of the waves is interpreted in terms of their attenuation with distance and decay with time as they propagate in the lossy plasma. The attenuation-length and decay-time constants of the waves are obtained, and their dependence on the incident-wave frequency and the gyrofrequency is examined. Optimum parameters for an experiment to detect these waves are suggested     

Study of fully developed wind wave spectrum by application of quantum statistics

The spectrum of fully developed wind waves is studied by application of the method of quantum statistics. A particle picture of water waves is introduced as an analogy of wave–particle duality. “Water wave particles” are conceived which are similar to phonons for elastic waves in solids. However, due to the property of wave breaking, the number of “water wave particles” in a quantum state is restricted. The spectrum of fully developed wind waves is studied on the basis of the maximum entropy principle. The similarity law of fully developed wind wave spectrum is proved. In the high frequency range, the spectral form is in agreement with the result of observations. In the particle picture, a saturated spectrum is introduced which is in conceptual consistency with the saturated spectrum introduced by Phillips in the wave picture, and the form of which is the same as Phillips’. It is further shown that in the high frequency range the spectrum is only half saturated for fully developed wind waves. The frequency downshifting phenomenon which cannot be explained by wave theory is explained in the particle picture.     

Scattering of light waves by electron electrostatic waves in laser produced plasmas

The propagation of light waves in an underdense plasma is studied using one-dimensional Vlasov-Maxwell numerical simulation.It is found that the light waves can be scattered by electron plasma waves as well as other heavily and weakly damping electron wave modes,corresponding to stimulated Raman and Brilluoin-like scatterings.The stimulated electron acoustic wave scattering is also observed as a high scattering level.High frequency plasma wave scattering is also observed.These electron electrostatic wave modes are due to a non-thermal electron distribution produced by the wave-particle interactions.The collision effects on stimulated electron acoustic wave and the laser intensity effects on the scattering spectra are also investigated.     

The analogy between acoustic waves and water surface waves with refraction

The similarity between acoustic waves in an inhomogeneous medium and water surface waves with variable water depth is established. The two systems are analogous if they both are characterized by the same index of refraction field. Based on this analogy, acoustic refraction problems are treated by utilizing a surface wave simulation achieved with a water wave tank. Experimental results obtained from the wave tank for various situations are used to deduce the behavior of the corresponding acoustic systems. It is concluded that there are two major advantages in employing a water wave tank. The first is that the entire wavefront configuration can visually be observed; the second is that water surface waves can be investigated in the laboratory much more readily and more economically than acoustic waves.     

Nonlinear three-wave interaction in marine sediments

Nonlinear interaction of three acoustic waves in a sandy sediment is studied in the frequency range where there is a considerable wave velocity dispersion. The possibility of an experimental observation of the generation of a sound wave by two pump waves propagating at an angle to each other is estimated.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。      

两层耦合可激发介质中螺旋波转变为平面波

采用Br-Eiswirth模型研究了两层耦合可激发介质中螺旋波的动力学,两层介质通过网络连接,即在每一层介质上,每一列选一个可激发单元作为中心点,在一层介质上同一列的可激发单元只与另一层介质上对应的中心点及其8个邻居有耦合.数值模拟结果表明:通过这种局部耦合,在适当小的耦合强度下两耦合螺旋波可实现同步,增大耦合强度会导致螺旋波漫游和漂移,造成螺旋波不同步,观察到螺旋波与静息态、低频平面波和不规则斑图共存现象.在适当强的耦合强度下,还观察到两螺旋波转变成同步的平面波消失现象.对产生这些现象的物理机理做了讨论.     

Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensatewith dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of ~/ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.